Ecological Interactions: an Application of Differential Equations — Presentation Detail — Celebration of Scholars

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Student presentations must have a faculty sponsor.

Abstracts must include a title and a description of the research, scholarship, or creative work. The description should be 150-225 words in length and constructed in a format or style appropriate for the presenter’s discipline.

The following points should be addressed within the selected format or style for the abstract:

A clear statement of the problem or question you pursued, or the scholarly goal or creative theme achieved in your work.
A brief comment about the significance or uniqueness of the work.
A clear description of the methods used to achieve the purpose or goals for the work.
A statement of the conclusions, results, outcomes, or recommendations, or if the work is still in progress, the results you expect to report at the event.

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Additional Information

More information is available at carthage.edu/celebration-scholars/. The following are members of the Research, Scholarship, and Creativity Committee who are eager to listen to ideas and answer questions:

Jun Wang
Kim Instenes
John Kirk
Nora Nickels
Andrew Pustina
James Ripley

Ecological Interactions: an Application of Differential Equations

Name: Marquell Williams
Major: Economics, Math
Hometown: Rockford, Illinois
Faculty Sponsor: Haley Yaple
Other Sponsors:
Type of research: Course project

Abstract

Ecological interactions are encounters and the resulting effects between different organisms within the same community, or the symbiotic relationships between Earth’s inhabitants. Few species live in isolation, and even fewer exhibit population growth patterns that do not involve interactions with other organisms. These ecological interactions are important as they determine Earth's biodiversity. We study three pairs of coupled differential equations involving three organisms in order to measure and predict changes in the aquatic ecosystem. The predator-prey, competition, and cooperation models of ecological interactions, collectively called the Kolmogorov models, offer accurate qualitative insight into population growth for many species. While these models predict population growth, analysis using differential equations allows for the determination of relative population changes in an ecosystem over time, and natural equilibrium points as a result of environmental factors and symbiotic relationships. Numerical solutions and analytical qualitative analysis are utilized to measure and predict changes within an ecosystem.

Poster file